The goal of this proposal is to develop statistical methods for environmental health data when the health effects of interest are complex. The Specific Aims are motivated by problems arising in toxicological and environmental epidemiological studies of the health effects of airborne particulate matter. Specific aims of the project are the development of (i) Wavelet-based historical functional data models for assessing high-dimensional associations between exposure and health;(ii) Hierarchical hidden Markov models for analyzing multivariate functional data arising from animal particulate matter concentrator studies;(iii) Methods to address exposure measurement error arising from spatial and temporal misalignment in particulate matter epidemiology studies. We will apply the proposed methods to several data sets for which existing analysis methods do not make full use of the data, including (i) semi-continuous heart- rate variability data from matter in sensitive subpopulations. In the motivating applications, the methods will provide insight into two scientifically pressing issues in environmental health research: the identification of biologic mechanisms of morbidity and mortality of air particles, and identification of pollution sources responsible for observed health effects. More generally, the proposed methods represent advancements in the areas of functional data analysis, hidden Markov modeling, and measurement error modeling that are applicable in a variety of biomedical research settings involving high-dimensional data.